# Cricket Wicket By Catch#

In a game of cricket akin to baseball, a batsman returns the ball bowled on a pitch and scores runs based on the distance travelled by the ball upon exiting the collision with the bat.

## Part 1#

If the ball leaves the bat with a speed of $$u\ \rm{m/s}$$ at an angle $$\alpha$$ measured up from the horizontal as shown in the image below, determine the value of $$$\dot{R}$$$$in$$\rm{m/s}$ as observed by a stationary spectator.

Treat the ball as a particle and assume an east-ward acceleration awind acting on the ball due to the wind.
$$\alpha = {{ params_a }}^\circ$$, $$u = {{ params_u }}\ \rm{m/s}$$, $$d = {{ params_d }}\ \rm{m}$$, $$a\_{wind} = {{ params_a_w }}\ \rm{m/s^{2}}$$.

Please enter in a numeric value in m/s.

## Part 2#

Determine the value of $$$\dot{\phi}$$$.

## Part 3#

Determine the value of $$$\dot{\theta}$$$.

## Part 4#

Determine the value of $$$\ddot{R}$$$.

Please enter in a numeric value in $$ms^{-2}$$.

## Part 5#

Determine the value of $$$\ddot{\theta}$$$.

Please enter in a numeric value in $$rads^{-2}$$.

## Part 6#

Determine the value of $$$\ddot{\phi}$$$.

Please enter in a numeric value in $$rads^{-2}$$.